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Comparison of Two Procedures for Predicting Rocket Engine Nozzle Performance

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Comparison of Two Procedures for Predicting Rocket Engine Nozzle Performance NASA Technical Memorandum 89814 0-' AIAA-87-207 1 I' t Comparison of Two Procedures for Predicting Rocket Engine Nozzle Performance Kenneth J. Davidian Lewis Research Center Cleveland, Ohio Prepared for the 23rd Joint Propulsion Conference cosponsored by the AIAA, SAE, ASME, and ASEE San Diego, California, June 29-July 2, 1987 COMPARISON OF TWO PROCEDURES FOR PREDICTING ROCKET ENGINE NOZZLE PERFORMANCE Kenneth J. Davidian National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135 Abstract layer prediction proqram used in this procedure. Unlike BLIMP, BLM is accompanied by a set of sub- Two nozzle performance prediction procedures programs which will calculate all the necessary whicn are based on the standardized JANNAF meth- preliminary information required for the boundary odology are presented and compared for four layer analysis. This total set of subprograms rocket engine nozzles. The first procedure (includinq BLM) is referred to as the 1985 ver- required operator intercedance to transfer data sion of the Two-Dimensional Kinetics program between the individual performance programs. The (TDK.85) .4 second procedure is more automated in that all necessary programs are collected into a single Performance comparisons were made for noz- computer code, thereby eliminating the need for zles having area ratios 60:1, 200:1, 400:1, and data reformatting. Results from both procedures 1OOO:l. Each nozzle had a throat diameter of co Lo show similar trends but quantitative differences. 1 in. and was specified to run at a chamber pres- d P) Agreement was best in the predictions of specific sure of 1000 psia using hydrogen and oxygen as I W impulse and local skin friction coefficient. the propellants. Variations of the wall temper- Other compared quantities include characteristic ature profile were made to investigate its effect velocity, thrust coefficient, thrust decrement, on the engine performance. boundary layer displacement thickness, momentum thickness, and heat loss rate to the wall. Description of Procedures Effects of wall temperature profile used as an input to the programs was investigated by running The first procedure for evaluating the three wall temperature profiles. It was found rocket engine nozzle performance is referred to that this change greatly affected the boundary as the disjoint procedure. The succession of layer displacement thickness and heat loss to the programs used in this procedure is the One- wall. The other quantities, however, were not Dimensional Equilibrium (ODE) program,5 the drastically affected by the wall temperature pro- One-Dimensional Kinetics (ODK) program,6 and the file change. Boundary Layer Integral Matrix Procedure program ( BLIMP).2 ODE is a thermochemical Droperties Introduction program which provided throat chemical composi- tion input data for the DDK proqram. ODK, a Accurate predictions of boundary layer kinetics program which computes finite rate reac- growth are necessary for accurate predictions in tion performance, was run from the nozzle throat rocket engine performance. Equilibrium and chem- to the exit. The results provide BLIMP with pres- ical kinetics programs already exist which pre- sure profile and chemistry information as input. dict performance losses with sufficient accuracy. The exclusion of a two-dimensional kinetics anal- However, the computer modeling of boundary layer ysis results from the fact that the 1973 version growth and its effect on rocket engine perform- of the Two-Dimensional Kinetics program (TDK.73) ance is less standardized. This is due to dif- was to be used, but it gave unstable results. ferences in the physical modeling and numerical Therefore, an average value for the equivalent procedures used. Boundary layer losses start to two-dimensional divergence efficiency of 0.996 detract greatly from the overall performance in was assumed in lieu of running TDK.73. This rocket engine nozzle designs with large exit-area divergence efficiency s equivalent to a 7.25' to throat-area ratios. These high area ratio divergence half-ang1e.j The flow diagram for nozzles (>400) are of interest for orbital trans- this procedure is shown in Fig. 1. Table 1 shows fer vehicles to obtain maximum performance as the required inputs for each program used in the indicated by high specific impulse. disjoint procedure and from which program (if any) they are generated. The purpose of this paper is to compare the results from two procedures for evaluating the The second procedure used is called the inte- performance of nozzle contours. Both procedures grated procedure. In this study, the integrated are based on the standardized JANNAF methodology1 procedure refers to a single program, the 1985 for predicting rocket engine nozzle performance. version of the TDK program (TDK.85). TDK.85 com- The first, the disjoint procedure, requires bines TDK.73 as a subproqram along with the transmission of data between three separate boundary layer module (BLM), ODE, ODK, and many performance prediction programs. The boundary other subprograms into one large program. The layer 8rediction program in this procedure is inputs required for the integrated procedure are BLIMP. BLIMP is an independent, stand-alone shown in Table 2. program and can only be utilized after prior runs of other performance programs. In this case, two Description of Programs programs were run as an input to BLIMP. The second, the integrated procedure, utilizes one The individual programs described below are performance program which ha many subroutines to performance prediction codes. perform the prediction. BLM 3 was the boundary 1 One-Dimensional Equilibrium Program (ODE)5 the kinetics variances in the nozzle downstream of the throat, and predicting the boundary layer This program calculates the equilibrium con- growth and losses. Also, the program can dis- ditions for a reactive mixture in an idealized place a potential wall contour hy the displace- closed combustion system. Reaction rates are ment thickness calculated by BLM and recompute considered to be infinitely fast so that all reac- the kinetic variances in the nozzle to attain a tions reach local equilibrium conditions. A better estimate of the boundary layer thickness. rocket performance option is run which predicts the theoretical maximum performance of isentropic Description of Input Cases convergent-subsonic and divergent-supersonic flow in a nozzle with shifting equilibrium chemical Four nozzles, with area ratios of 60:1, composition during expansion. The results from 200:1, 400:1, and 1000:1, were chosen for this ODE were used as throat condition inputs to the evaluation study. All four had 0.5 in. throat ODK program in the disjoint procedure. raiii and lengths corresponding to a 100 percent 15 cone with the same throat radius and area One-Dimensional Kinetics Program ( ODK)6 ratio.’l They all operated at 1000 psia chamber pressure and used normal boiling point (NBP) liq- This program calculates the deviation from uid hydrogen and NBP liquid oxygen as their fuel equilibrium performance in the nozzle due to and oxidizer. The propellants were injected with finite reaction rates not allowing chemical equi- a mixture ratio (O/F) of six. librium to be reached. Unlike ODE, ODK bases the fraction of mixture which will react on the reac- For the given area ratios, the nozzle exit tion rates of the mixture. ODK considers complex, radii were determined. These exit plane lengths homogeneous, ideal gas reactions in combustion and radii values are tabulated in Table 4. Since and nozzle expansion situations. Eighteen chemi- the purpose of this study was comparative in cal reactions and four three-body recombination- nature, the actual contour of the nozzles was not dissociation reactions were used by ODK for the important so long as they were the same for both fuelloxygen combination of hydrogen and oxygen procedures. The contour for each nozzle between (Table 3). The output from this program provides the throat and exit plane was calculated using an axial pressure profile along a streamline the RAO method, a method of characteristics rou- boundary (i.e. the nozzle wall) as an input to tine coupled with an optimization scheme based on the BLIMP program in the disjoint procedure. ODK the calculus of variations.8 These contours also outputs performance results including speci- (Appendix A) defined the potential flow bound- fic impulse, thrust coefficient (CF), and char- aries for each nozzle. acteristic velocity (c*). The remaininq operating conditions of the Boundary Layer Integral Matrix Procedure Program engine were used as inputs for ODK, BLIMP, and (BLIMP) TDK. The energy level associated with the oxygen is -2948 callmole and -1977 callmole for the This program calculates the boundary 1 ayer hydrogen. The geometry variables of the combus- growth in a rocket nozzle. For axisymmetric tion chamber, throat, and nozzle are shown in flow, the program can calculate either shifting Fig. 2 and the corresponding values are specified equilibrium or frozen compositions for any fuel/ in Table 5. oxidizer combination. The program uses an inte- gral matrix solution algorithm which is equivalent For both evaluation procedures, the poten- to a higher order finite difference approach. tial wall contour was defined by specifying axial This program will output various boundary layer location values and radii at equal intervals properties as well as the coordinates of the along the nnzzle centerline. In the integrated potential flowfield if the input described the procedure, the number of contour points was real wall, or the coordinates of the.real wall if greatly reduced at the higher area ratios (>200:1) the potential flow contour was input. to insure that the contour interpolating routine would not compute an erratic wall slope between Two-Dimensional Kinetics Program 1983 Version input wall points. The number of points given ITDK. 83)j for each area ratio for both procedures, the num- ber of points on the sonic line at the throat This program is really a combination of pro- (required to set-up the method of characteristics grams.
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